You are given a permutation$$$^{\dagger}$$$ $$$p$$$ of length $$$n$$$.

We call index $$$x$$$ good if for all $$$y \lt x$$$ it holds that $$$p_y \lt p_x$$$ and for all $$$y \gt x$$$ it holds that $$$p_y \gt p_x$$$. We call $$$f(p)$$$ the number of good indices in $$$p$$$.

You can perform the following operation: pick $$$2$$$ distinct indices $$$i$$$ and $$$j$$$ and swap elements $$$p_i$$$ and $$$p_j$$$.

Find the maximum value of $$$f(p)$$$ after applying the aforementioned operation exactly once.

$$$^{\dagger}$$$A permutation of length $$$n$$$ is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array), and $$$[1,3,4]$$$ is also not a permutation ($$$n=3$$$ but there is $$$4$$$ in the array).

Input

Each test consists of multiple test cases. The first line of contains a single integer $$$t$$$ ($$$1 \le t \le 2 \cdot 10^4$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$) — the length of the permutation $$$p$$$.

The second line of each test case contain $$$n$$$ distinct integers $$$p_1, p_2, \ldots, p_n$$$ ($$$1 \le p_i \le n$$$) — the elements of the permutation $$$p$$$.

It is guaranteed that sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output a single integer — the maximum value of $$$f(p)$$$ after performing the operation exactly once.

Note

In the first test case, $$$p = [1,2,3,4,5]$$$ and $$$f(p)=5$$$ which is already maximum possible. But must perform the operation anyway. We can get $$$f(p)=3$$$ by choosing $$$i=1$$$ and $$$j=2$$$ which makes $$$p = [2,1,3,4,5]$$$.

In the second test case, we can transform $$$p$$$ into $$$[1,2,3,4,5]$$$ by choosing $$$i=1$$$ and $$$j=2$$$. Thus $$$f(p)=5$$$.

Field Should Not Be Empty

Examples